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Appendix II.                             881

Again, suppose the air to be compressed from i to x atmospheres,

Raising to the tI power,


- 1 y

We may deduce some important results from the last two
. If a gas be compressed or expanded in any manner,
then returned to the original temperature, the heat supplied
^ removed must equal the work area as indicated, for the internal
**ergy is then unchanged. Fig. 841 is a general diagram for air-

Compressor and motor, and we may take three cases:

f Adiabatic compression: coaikag back to isothermal:
I J                                                      heat lost...  == H-f-C

!. Adiabatic expansion: work gained (from gas)    = H-M
.-. Total loss in system = (H 4- C) - (H - M) = C -h M

TT j" Isothermal compression : no cooling: heat lost = H
I Adiabatic expansion:              work gained ...  = H - M

..  Total loss in system = H - (H - M)   = M
(Isothermal compression :               heat Ipst...  =  H

I- \ _              .           .        fheattobesupplied=H) ,

I Isothermal expansion:^     i     .   /r       TT Uoss =  o
1            ^work gamed     ... =HJ

. .  Total loss in system ... = H

The isothermal line is most closely approached by two-stage
:ompressors (p. 547), and by two-stage motors, whose diagrams
ore given at A and B respectively, Fig. 841; but in the second it
be understood that all the external work must be supplied